As one of memory systems, there is a NAND flash memory including a NAND type memory cell. In the NAND flash memory, since electrons are caused to forcibly pass through a tunnel oxide film at the time of erasing or at the time of programming, the tunnel oxide film gradually deteriorates. Further, due to a tunnel effect or hopping, electrons leak through a floating gate. In addition, accumulated electrons trapped in the tunnel oxide film tend to be discharged over time. These phenomena cause a problem of expanding the distributions of erase potential and write potential and lowering a proof stress against retention.